Can AI replace LanguageTool?

Build me a local grammar checker to replace LanguageTool Premium. Requirements:

- Do not reimplement the checker: run the open-source LanguageTool server locally
  (the Java 17 jar, skip Docker) on localhost:8081, started by a wrapper script.
- A CLI: `check file.md` prints issues with line numbers, grouped by rule category,
  and exits nonzero when errors are found so it works as a pre-commit hook.
- A tiny web page on localhost:4860 (Express, one textarea): paste text, see
  underlined issues with suggested fixes, click a suggestion to apply it.
- Optional LLM rewrite button: send a paragraph plus the LanguageTool findings to
  Claude or GPT (key in .env) and show the corrected version as a diff.
- Personal dictionary in a plain words.txt that the server loads, so my names and
  jargon stop flagging.
- A setup script that downloads the LanguageTool release zip, and optionally the
  n-gram data. Warn in the README: the n-gram files are about 8 GB but catch far
  more real errors.
- Everything runs locally and works offline except the optional LLM call. No
  accounts, no telemetry.
- Out of scope: browser extensions and the premium-only rules. The open rule set is
  what we get.
- README: Java install, memory flags for the server, and wiring the CLI into git
  hooks.